The present invention relates to on-board optimization techniques for on-board control, and is particularly useful for Model Predictive Control of a dynamical system.
This invention describes a significant enhancement to existing optimization techniques for on-board control. On-board Model Predictive Control of a nonlinear dynamical system often involves linearizing the nonlinear dynamics and posing a Quadratic Program to stay close to a desired profile of outputs. Since on-board control requires computing a reliable solution in a robust manner in real-time, the quadratic programming algorithm needs to use linear algebra optimally.
Model Predictive Control refers to the procedure of determining optimal operating parameters of a dynamic process based on a model of the ‘plant,’ or the dynamical system. This plant model can be a physics-based model of anything ranging from a gas turbine engine to the acoustics inside a helicopter. It is of interest to engineers to operate such a plant optimally, i.e. meet or exceed certain goals during operation, while honoring physical constraints of the system. To this end, it is common to solve a constrained optimization problem during the operation of the plant, and update the parameters of the optimization problem as the system evolves in time or as the forecast of the future requirements change, and re-solve the problem.
A significant difficulty in this procedure is the need to be able to obtain a reasonable solution for a complex optimization problem in real-time, which is the issue addressed by this invention.
In the past, real-time control has been attempted in chemical engineering applications, particularly in real-time process control. It has also been applied in real-time trajectory planning in aerospace applications. However, the optimization problems arising therein needed to be solved in several minutes, often even hours.
The ‘real-time’ scale allowed by problems of interest here are on the order of milliseconds. The novel algorithm described herein is capable of addressing this time requirement, without sacrificing the fidelity of the solution, and is thus a significant enhancement to existing methods.
Co-pending application, U.S. Ser. No. 10/308,285, filed Dec. 2, 2002, and entitled Real-Time Quadratic Programming for Control of Dynamical Systems, is commonly assigned and one of the inventors is also the inventor of the present application. The problem that invention mainly addresses is the ‘Dynamic Inversion’ control problem spanning over only one time step and with a much smaller budget for computation, and hence a different strategy was used in performing the active set hot start. Further, a different procedure was used for dropping constraints during the search for the active set, which consequently required different linear algebra. Though quite different, the method described in this invention can also be an alternate method for solving the quadratic programming algorithm for Dynamic Inversion (though it may not be the better method for Dynamic Inversion).